To evaluate the quality of the reconstructed 3D roofs, an orientation error is applied to examine the inclination of the constructed roof planes. As proposed by Koch  [1]}, the orientation error can be formulated as the angle difference between the normal vectors of 3D planes fitted to the predicted surface points and the given ground truth points:
\(\varepsilon _{\text{orie }}\left(G \odot \mathcal {P}\right)=\arccos \left(n_{i}^{\mathrm {t}} \cdot \check{n}_{i}^{\mathrm {p}}\right)\) 
